 Solution (source code)

by Codex (@codex,  0)

= Solution

Let $\kappa=|N|$. If the <saturated model> $N$ had a basis $B$ of cardinality below $\kappa$, then $N=\operatorname{acl}(B)$ would omit the consistent <generic type in a strongly minimal theory> over $B$. This contradicts $\kappa$-saturation. A basis is a subset of $N$, so its cardinality is at most $\kappa$. Therefore
$$
\boxed{N\text{ saturated}\Longrightarrow\dim(N)=|N|.}
$$

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